## anonymous one year ago What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6? f(x) =negative one over six times x squared plus four over three times x plus eleven over six f(x) =one over six times x squared minus four over three times x minus eleven over six f(x) = three fiftieth x squared plus eleven twenty fifth x plus three fifth f(x) = two fiftieth x squared plus eleven twenty fifth x plus two fifth

1. anonymous

@welshfella @nincompoop @Nnesha @ganeshie8

2. anonymous

3. Nnesha

first we should draw a point at (4,-3) and horizontal line y=-6 |dw:1442578792483:dw| this one is better

4. anonymous

|dw:1442578889393:dw|

5. Nnesha

|dw:1442578826480:dw| yes that's right :=)

6. Nnesha

brb wait a mint plz

7. Nnesha

sorry about alright so now we should pick a point to find distance between the point and focus and distance between the point and directrix you can pick any point |dw:1442579344198:dw|

8. Nnesha

equation would be like this $\huge\rm \sqrt{(x-a)^2+(y-b)^2} =\sqrt{ (y-c)^2}$ c = directrix (a,b) is a focus point (4,-3) now substitute a ,b c for their values

9. anonymous

square root 4-a^2+-3-b=square root-3-c^2

10. Nnesha

well (x,y) is a point that we picked we supposed taht (a,b) is the focus point so replace a with 4 b with -3 and c with -6 c is directix

11. anonymous

4-4^2+-3-(-3)=square root-3-(-6)^2 like this?

12. Nnesha

keep the x and y variable $\large\rm \sqrt{(x-4)^2+(y-(-3))^2} =\sqrt{ (y-(-6))^2}$ like this now take square both sides to cancel out the square root

13. anonymous

X^-16+Y+9=Y+36

14. anonymous

X^2

15. anonymous

is that right

16. Nnesha

hmm no (x-4)^2 = ?

17. anonymous

X^2+16

18. Nnesha

hmm no (x-4)^2 is same as (x-4)(x-4) foil it signs are the same in the parentheses so you should get 3 terms

19. anonymous

X^2-8x+16

20. Nnesha

yes right $x^2-8x+16+(y-(-3))^2=(y-(-6))^2$ foil (y-(-3))^2 and then right side

21. Nnesha

here is a hint you will get two terms when you have (a-b)(a+b) opposite signs

22. anonymous

Y^2-9

23. Nnesha

hmm no (y-(-3))^2 first distribute -1(-3) ?

24. anonymous

thats 3

25. Nnesha

yes so (y+3)^2 is same as (y+3)(y+3)

26. anonymous

oh

27. anonymous

y^2+6y-9

28. anonymous

+9

29. Nnesha

yes right $\large\rm x^2-8x+16+y^2+6y+9=(y-(-6))^2$ foil right side

30. anonymous

Y^2+12y+36

31. anonymous

i dont mean to rush but i have to go soon

32. Nnesha

yes right $\large\rm x^2-8x+16+y^2+6y+9=y^2+12y+36$ foil right side now simplify combine like terms

33. Nnesha

well it will takes some time we need to apply the complete the square method .....

34. Nnesha

$\large\rm x^2-8x+\color{red}{16}+\color{blue}{y^2}+6y+\color{red}{9}=\color{blue}{y^2}+12y+36$ combine like terms at left side and then move y^2 to the right side let me know what you get

35. anonymous

srry but i have to go thank you any ways

36. Nnesha

okay we will finish this whnevr u hve time

37. princesssleelee

@Nnesha i have this question as well that i need assistance with.